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Research Papers: Contact Mechanics

# Closed-Form Equations for Three Dimensional Elastic-Plastic Contact of Nominally Flat Rough Surfaces

[+] Author and Article Information
Ali Sepehri, Kambiz Farhang

Department of Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, IL 62901

J. Tribol 131(4), 041402 (Sep 23, 2009) (8 pages) doi:10.1115/1.3204775 History: Received April 07, 2007; Revised July 15, 2009; Published September 23, 2009

## Abstract

Approximate closed-form equations governing the shoulder-shoulder contact of asperities are derived based on a generalization by Chang, Etsion, and Bogy. The work entails the consideration of asperity shoulder-shoulder contact in which the volume conservation is assumed in the plastic flow regime. Shoulder-shoulder asperity contact gives rise to a slanted contact force comprising tangential and normal components. Each force component comprises elastic and plastic terms, which upon statistical summation yields the force component for the elastic and plastic forces for the contact of two rough surfaces. Half-plane tangential force due to elastic-plastic contact is derived through the statistical summation of tangential force component along an arbitrary tangential direction. Two sets of equations are found. In the first set of equations the functional forms are simpler and provide approximation of contact force to within 9%. The second set is enhanced equations derived from the first set of approximate equations that achieve an accuracy of within 0.2%.

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## Figures

Figure 1

Contacting rough and flat surfaces using the plastic asperity concept

Figure 2

Elastic-plastic contact of two rough surfaces; for wc2<wc1, elastic-plastic behavior would be dominated by surface 2

Figure 3

Interference showing normal and oblique elastic-plastic force terms and components

Figure 4

Contact of two rough surfaces with considering plastic fictitious surfaces

Figure 5

Dimensionless total normal force for wc=0.5; contour lines for various βs (shown as Bs)

Figure 6

Dimensionless total half-plane tangential force for wc=0.5; contour lines for various βs (shown as Bs)

Figure 7

ENp(h,βs) for wc=0.5 (Eq. 51)

Figure 8

EN(h,βs) for wc=0.5

Figure 9

EN(h,βs) for wc=0.5

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